Uniform Interpolation in provability logics

Marta Bilkova

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arXiv · 2211.02591

Uniform Interpolation in provability logics

Marta Bilkova

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Abstract

We prove the uniform interpolation theorem in modal provability logics GL and Grz by a proof-theoretical method, using analytical and terminating sequent calculi for the logics. The calculus for G\"odel-L\"ob's logic GL is a variant of the standard sequent calculus, in the case of Grzegorczyk's logic Grz, the calculus implements an explicit loop-preventing mechanism inspired by work of Heuerding.

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Marta Bilkova. 2022-11-04. Uniform Interpolation in provability logics. https://arxiv.org/abs/2211.02591

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